for any set of finite perimeter \(A\subset \mathbb {H}^2\) , see [1]}, [2]}, [3]} dealing with sets with smooth boundary, the extension to sets of finite perimeter can be obtained with standard approximation arguments. Moreover, we recall that geodesic balls realize the equality in (REF ). From (REF ) we easily deduce that
\(\frac{\mathrm {Per}(A)}{\mathfrak {m}(A)}\ge 1,\) 
